If $a = 12-3\cdot 2$ and $ b = 5 + 2^2$, what is $\frac{a^2}{b}$?
$a = 12-6 = 6$ and $b = 5 +4 = 9$. So, $\frac{a^2}{b} = \frac{36}{9} = \boxed{4}$.